It published an interim order stating they would need "prior written consent" from the UK regulator before making acquisitions between the companies.

The order applies to the businesses as well as their subsidiaries.

It comes two weeks after the regulator blocked Microsoft's $68.7bn (£54.8bn) deal to buy Activision Blizzard.

The takeover would have seen Microsoft acquire such hit titles as Call of Duty, Overwatch and World of Warcraft.

But the regulator said it was concerned the deal would offer reduced innovation and less choice for gamers in the cloud gaming business.

Microsoft and Activision criticised the decision and said they would appeal, with an Activision official saying at the time it showed the UK was "clearly closed for business".

To go through, the deal has to be approved by regulatory bodies in the UK, United States and European Union.

The CMA was the first regulator to make a ruling, in April. The EU is expected to make a decision in May.

In the interim order, the CMA wrote it was "preventing pre-emptive action" from Microsoft or Activision Blizzard.

The order prevents the businesses from acquiring an interest in each other, including their subsidiaries, or businesses that themselves have interest in the companies.

For example:

*  Activision Blizzard could not invest in Microsoft's Xbox Game Studios

*  Microsoft could not invest in Activision Blizzard subsidiaries such as King, the studio that makes hit mobile game Candy Crush Saga

The order states the companies should "immediately notify the CMA" if they have "any reason to suspect" the order has been breached.

A Microsoft official told BBC News: "We remain firmly committed to this deal and look forward to presenting our case to the Competition Appeal Tribunal."

Activision Blizzard has been approached for comment.